Quantum Computing: A Short Course from Theory to Experiment

Quantum Computing: A Short Course from Theory to Experiment

Description

The result of a lecture series, this textbook is oriented towards students and newcomers to the field and discusses theoretical foundations as well as experimental realizations in detail. The authors are experienced teachers and have tailored this book to the needs of students. They present the basics of quantum communication and quantum information processing, leading readers to modern technical implementations. In addition, they discuss errors and decoherence as well as methods of avoiding and correcting them.

About the Author

Prof. D. Suter is an experimentalist and well known for his NMR-work and currently working on quantum computation projects. He worked with Nobel laureate Ernst RR in Zurich.

Also Prof. J. Stolze is known to be a good teacher. As a theorist, his topic research area is quantum spin chains.

8.2 The Deutsch algorithm: Looking at both sides of a coin at the same time.

8.2.1 Functions and their properties.

8.2.2 Example: one-qubit functions.

8.2.3 Evaluation.

8.2.4 Many qubits.

8.2.5 Extensions and generalizations.

8.3 The Shor algorithm: It’s prime time.

8.3.1 Some number theory.

8.3.2 Factoring strategy.

8.3.3 The core of Shor’s algorithm.

8.3.4 The quantum Fourier transform.

8.3.5 Gates for the QFT.

8.4 The Grover algorithm: Looking for a needle in a haystack.

8.4.1 Oracle functions.

8.4.2 The search algorithm.

8.4.3 Geometrical analysis.

8.4.4 Quantum counting.

8.4.5 Phase estimation.

8.5 Quantum simulations.

8.5.1 Potential and limitations.

8.5.2 Motivation.

8.5.3 Simulated evolution.

8.5.4 Implementations.

9 How to build a quantum computer.

9.1 Components.

9.1.1 The network model.

9.1.2 Some existing and proposed implementations.

9.2 Requirements for quantum information processing hardware.

9.2.1 Qubits.

9.2.2 Initialization.

9.2.3 Decoherence time.

9.2.4 Quantum gates.

9.2.5 Readout.

9.3 Converting quantum to classical information.

9.3.1 Principle and strategies.

9.3.2 Example: Deutsch–Jozsa algorithm.

9.3.3 Effect of correlations.

9.3.4 Repeated measurements.

9.4 Alternatives to the network model.

9.4.1 Linear optics and measurements.

9.4.2 Quantum cellular automata.

9.4.3 One-way quantum computer.

10 Liquid state NMR quantum computer.

10.1 Basics of NMR.

10.1.1 System and interactions.

10.1.2 Radio frequency field.

10.1.3 Rotating frame.

10.1.4 Equation of motion.

10.1.5 Evolution.

10.1.6 NMR signals.

10.1.7 Refocusing.

10.2 NMR as a molecular quantum computer.

10.2.1 Spins as qubits.

10.2.2 Coupled spin systems.

10.2.3 Pseudo / effective pure states.

10.2.4 Single-qubit gates.

10.2.5 Two-qubit gates.

10.2.6 Readout.

10.2.7 Readout in multi-spin systems.

10.2.8 Quantum state tomography.

10.2.9 DiVincenzo’s criteria.

10.3 NMR Implementation of Shor’s algorithm.

10.3.1 Qubit implementation.

10.3.2 Initialization.

10.3.3 Computation.

10.3.4 Readout.

10.3.5 Decoherence.

11 Ion trap quantum computers.

11.1 Trapping ions.

11.1.1 Ions, traps and light.

11.1.2 Linear traps.

11.2 Interaction with light.

11.2.1 Optical transitions.

11.2.2 Motional effects.

11.2.3 Basics of laser cooling.

11.3 Quantum information processing with trapped ions.

11.3.1 Qubits.

11.3.2 Single-qubit gates.

11.3.3 Two-qubit gates.

11.3.4 Readout.

11.4 Experimental implementations.

11.4.1 Systems.

11.4.2 Some results.

11.4.3 Problems.

12 Solid state quantum computers.

12.1 Solid state NMR/EPR.

12.1.1 Scaling behavior of NMR quantum information processors.

12.1.2 31P in silicon.

12.1.3 Other proposals.

12.1.4 Single-spin readout.

12.2 Superconducting systems.

12.2.1 Charge qubits.

12.2.2 Flux qubits.

12.2.3 Gate operations.

12.2.4 Readout.

12.3 Semiconductor qubits.

12.3.1 Materials.

12.3.2 Excitons in quantum dots.

12.3.3 Electron spin qubits.

13 Quantum communication.

13.1 “Quantum only” tasks.

13.1.1 Quantum teleportation.

13.1.2 (Super-) Dense coding.

13.1.3 Quantum key distribution.

13.2 Information theory.

13.2.1 A few bits of classical information theory.

13.2.2 A few bits of quantum information theory.

Appendix.

A. Two spins-1/2: Singlet and triplet states.

B. Symbols and abbreviations.

Bibliography.

Index.

It's a very good book - it's by far the best textbook at this level, and will become the principal text for our new course.

Jonathan Jones Oxford Centre for Quantum Computation

"The authors, experimantalists, being themselves involved in the realization of quantum computers, present with this book a didactically well formed introduction to quantum information processing, including computer architecture, tested and proposed schemes. Clearly, in order to offer this extensive material in a space of only just over 200 pages, the authors had restricted themselves to basic of relevant ideas. The latter are well selected and guide readers attention engagingly in chosen directions. ... This textbook has the advantage that it contains both, theoretical as well as experimental, features of quantum computing, that the exposition is well organized, and for beginners that it omits more advanced mathematical tools. It gives ... a broad overview ... It is an introduction for beginners, a good one, and can be well recommended as such." Zentralblatt MATH